Most states do not insist a driver to make a police report after they have hit a deer, but state laws differ so you will need to check with your state's Department of Motor Vehicles, or similar agency, to find out what your state requires. Even if you are not commanded to make a police report, it is wise to do so if you need to make an insurance claim regarding damage caused hitting the deer thru your comprehensive portion of your policy.
If you want to keep the deer carcass generally states do require you to report the accident with authorities. In Pennsylvania you must report taking the possession of the deer to the Game Commission. In Ohio you need to report it to the game protector or a law enforcement officer. If you do not want to keep the deer's body it is helpful to other drivers if you will call the state patrol, sheriff or state wildlife agency so that the carcass can be removed from the roadway area.